Students from Korea at the London School of Economics in London. Theresa May's policies are likely to lead to 260,000 fewer overseas students coming to the UK over the next five years. Photograph: Sarah Lee for the Guardian

The home secretary, Theresa May, has refused to accept an official "impact assessment" which put the cost to Britain's economy of her curbs on overseas students at up to £3.6bn.

May has dismissed her own department's official assessment of the impact of her policy on overseas student visas, and has instead asked the migration advisory committee for a "better assessment and a better judgment of the true picture".

Her actions are strongly criticised by MPs on the Commons home affairs select committee, who say it confirms their "deep concerns" that Home Office ministers are not taking "evidence-based policy" as seriously as they could.

The MPs say that the disputed impact assessment – which warns of the £2.4bn cost to the British economy of curbing overseas student visas – was not published until 12 weeks after the policy was announced, despite ministerial promises.

"We were disappointed that the impact assessment was so delayed in this instance and call on the Home Office to take measures to ensure the situation does not recur," says the home affairs select committee follow-up report on student visas published on Tuesday.

The government expects 260,000 fewer study visas to be issued to non-EU students over the next five years as a result of the changes.

By the next general election, ministers have pledged to reduce overall annual net migration to the "tens of thousands".

The impact assessment estimates that, in its "worst-case scenario", the new policy will have a net cost of £3.2bn over the next four years in reduced economic output and a further £330m in lost tuition and immigration visa fees.

It gives a "central estimate" of £2.4bn net lost and a "best-case scenario" of £1.3bn lost.

The home secretary has told MPs she does not believe these estimates as they do not take full account of the costs to public services, and – "crucially" – make an assumption that if a student does not come with a visa and work in Britain, that job will not be filled by anyone else.

She said: "I have asked the migration advisory committee – and I am not going to pluck at figures from thin air – to look at these issues to see if we can get to a point where we can get a better assessment and a better judgment of the true picture, in relation to the costs or otherwise of the decisions that we are taking, because I do not believe that the impact assessment gives a full and true picture at the moment."

But the MPs on the home affairs committee say the impact assessment may in fact be underestimating, rather than overestimating, the costs, because it assumes that eight out of 10 places left vacant in further education colleges and English language schools by overseas students would be filled by other EU nationals or British students, without any loss of income.

The MPs say it is questionable how easy it will be to fill these student places.

Keith Vaz, the chairman of the committee, said: "The home secretary's dismissal of the impact assessment is very disappointing.

"The government appears to be not only making policy without adequate immigration statistics, but also ignoring its own evidence.

"We reiterate the need for an immigration policy which is both evidence-based and does not adversely affect the British economy."

In an official response to the committee, the immigration minister, Damian Green, said he agreed that any changes in student immigration policy ought to be accompanied by a publicly available impact assessment.

Green said the "tough measures" on student visas were necessary not only to tackle the problems of bogus colleges and deter bogus students, but also to provide proper control of the overseas student route.

The package of measures includes a system of licensed colleges, stricter English language requirements and restrictions on working rights and the ability to bring dependents to Britain.

The consultation on the package provoked 31,000 responses – one of the largest since the coalition came to power.